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Chin. Phys. B, 2025, Vol. 34(11): 117501    DOI: 10.1088/1674-1056/ae00ad
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High-frequency complex permeability calculation for metallic soft magnetic particles with easy magnetization plane in non-magnetic medium

Liangrui Tan(谭梁睿)1, Donglin He(何东霖)1, Zhibiao Xu(徐志彪)1, Guowu Wang(王国武)2, Shengyu Yang(杨晟宇)1, Shaoyong Leng(冷绍勇)1, Ruilong Li(李睿龙)1, and Tao Wang(王涛)1
1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Ninth Institute, China Electronics Technology Group Corporation, Mianyang 621000, China
Abstract  Soft magnetic composites made from metallic magnetic particles with an easy magnetization plane (referred to as easy-plane metallic soft magnetic composites (SMC)) are considered ideal materials for the next generation of power electronic devices. This advantage is attributed to their ability to maintain high permeability at elevated frequencies. Despite these advantages, a definitive mathematical model that connects the high-frequency magnetic properties (e.g., effective permeability) of easy-plane metallic SMCs to the intrinsic properties of the particles is still lacking. In this work, a theoretical calculation model for the effective permeability of easy-plane metallic SMCs was formulated. This model was derived from a skin effect-corrected Landau-Lifshitz-Gilbert (LLG) equation and integrated with effective medium theory incorporating inter-particle interaction. To validate the model, we prepared samples of easy-plane Y$_{2}$Co$_{17}$ particle/PU SMCs with varying particle sizes and volume fractions. The experimental results showed a strong agreement with the calculated values. This research offers critical theoretical backing for the design and optimization of soft magnetic materials intended for high-frequency applications.
Keywords:  easy-plane material      high-frequency      soft magnetic composites      complex permeability      Landau-Lifshitz-Gilbert (LLG) equation  
Received:  04 June 2025      Revised:  30 July 2025      Accepted manuscript online:  29 August 2025
PACS:  75.40.Gb (Dynamic properties?)  
  85.70.-w (Magnetic devices)  
  85.70.Ay (Magnetic device characterization, design, and modeling)  
Fund: This work was supported by the National Key R&D Program of China (Grant No. 2021YFB3501300), the 9th Research Institute of China Electronics Technology Group Corporation’s open projects (Grant No. 2024SK-002-01), and the Science and Technology Project of Gansu Province (Grant No. 22YF7GA001).
Corresponding Authors:  Jurong Zhang     E-mail:  wtao@lzu.edu.cn
About author:  2025-117501-250983.pdf

Cite this article: 

Liangrui Tan(谭梁睿), Donglin He(何东霖), Zhibiao Xu(徐志彪), Guowu Wang(王国武), Shengyu Yang(杨晟宇), Shaoyong Leng(冷绍勇), Ruilong Li(李睿龙), and Tao Wang(王涛) High-frequency complex permeability calculation for metallic soft magnetic particles with easy magnetization plane in non-magnetic medium 2025 Chin. Phys. B 34 117501

[1] Xu Z B, Wang G W, Zhang S, Cui J H, Xiong L H, He D L, Liu Y and Wang T 2025 Appl. Phys. Lett. 126 082404
[2] Zheng Z L, Feng Q Y, Xiang Q Y, Di Z X and Harris V G 2017 J. Appl. Phys. 121 063901
[3] Shirakata Y, Hidaka N, Ishitsuka M, Teramoto A and Ohmi T 2008 IEEE Trans. Magn. 44 2100
[4] Huang Y D, Zhang H, Shang R X, Wang K, Wu P, Wang Y, Li F S and Wang T 2023 J. Phys. D: Appl. Phys. 56 065004
[5] Li H, Serrano D, Wang S, Guillod T, Luo M and Chen M 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), March 19-23, 2023, Florida, USA, p. 1543
[6] Shen X, Zuo Y, Kong J and Martinez W 2024 IEEE Trans. Power Electron. 39 8478
[7] Zhu Y Y 2023 J. Magnet. Magnet. Mater. 570 170535
[8] Wang Y, Zhang P, Li K, Xin T, Yang W, Liu S, Han J, Du H, Wang C, Luo Z and Yang J 2025 J. Magnet. Magnet. Mater. 613 172677
[9] Wang P 2021 High-frequency Magnetic and Microwave Absorbing Properties of Rare Earth-transition Metal Alloy Fractured Along Easy- Magnetization Crystal Plane (Ph.D.Dissertation) (Lanzhou: Lanzhou University) (in Chinese)
[10] Gutfleisch O, Willard M A, Brück E, Chen C H, Sankar S G and Liu J P 2011 Adv. Mater. 23 821
[11] Périgo E A,Weidenfeller B, Kollár P and Füzer J 2018 Appl. Phys. Rev. 5 031301
[12] Silveyra J M, Ferrara E, Huber D L and Monson T C 2018 Magnet. Mater. 362 6413
[13] Krings A, Boglietti A, Cavagnino A and Sprague S 2017 IEEE Trans. Ind. Electron. 64 2405
[14] Rozanov K N, Li Z W, Chen L F and Koledintseva M Y 2005 J. Appl. Phys. 97 13905
[15] Xue D S, Li F S, Fan X L and Wen F S 2008 Chin. Phys. Lett. 25 4120
[16] Wang P, Zhang J,Wang G, Duan B, Wang T and Li F 2020 Appl. Phys. Lett. 116 112403
[17] Wang K, Zhang H, Huang Y D, Xu Z B, Li F S and Wang T 2024 J. Rare Earths 42 110
[18] Xu Z B, Zhang S, Cui J H, He D L,Wang K, Zhao J J, Liu Y andWang T 2024 J. Magnet. Magnet. Mater. 609 172476
[19] Zhang H,Wang K, Huang Y D, Zhang C H,Wang Y andWang T 2023 J. Magnet. Magnet. Mater. 588 171471
[20] Wan W, Wu C, Liu G, Chen Q and Yan M 2024 AIP Adv. 14 055213
[21] Han Y, Wang G W, Xu Z B, Wang K, He D L, Wang Y and Wang T 2024 J. Magnet. Magnet. Mater. 609 172467
[22] Yin H M and Sun L Z 2005 Phys. Rev. B 72 054409
[23] Romeis D and Saphiannikova M 2023 J. Magnet. Magnet. Mater. 565 170197
[24] Ntinger B 1994 Trans. Porous Media 15 99
[25] Le Floc’h M, Mattei J L, Laurent P, Minot O and Konn A M 1995 J. Magnet. Magnet. Mater. 140-144 2191
[26] King P R 1989 Trans. Porous Media 4 37
[27] Rousselle D, Berthault A, Acher O, Bouchaud J P and Zérah P G 1993 J. Appl. Phys. 74 475
[28] Bregar V B 2005 Phys. Rev. B 71 174418
[29] Bregar V B and Pavlin M 2004 J. Appl. Phys. 95 6289
[30] Waki H, Igarashi H and Honma T 2005 IEEE Trans. Magn. 41 1520
[31] Liu G, Wang K, Zhang X, Liu H, Luo W, Jin J, Yan M and Wu C 2026 J. Mater. Sci. Technol. 245 197
[32] Wang K, Liu G, Gong J, Wang L, Chen Q, Zhang X, Zhang Z, Yan M and Wu C 2025 Small 21 2501547
[33] Wu L Z, Ding J, Jiang H B, Neo C P, Chen L F and Ong C K 2006 J. Appl. Phys. 99 083905
[34] Li T, Shi H G, Jin X W and Xue D S 2021 J. Magnet. Magnet. Mater. 536 168122
[35] Gilbert T L 2004 IEEE Trans. Magn. 40 3443
[36] Choy T C 2016 Effective Medium Theory: Principles and Applications (Oxford: Oxford University Press)
[37] Markel V 2016 J. Opt. Soc. America A 33 1244
[38] Zhong J, Tan G, Man Q, Ning M, Gao Y, Liu X and Pan J 2021 J. Mater. Sci.: Mater. Electron. 32 27849
[39] Andreev A V, Tereshina E A, Gorbunov D I, Šantavá E, Šebek J, Ž áček M, Daniš S, Pospíšil J and Havela L 2015 J. Alloys Compd. 621 415
[40] Zhang H, Huang Y D, Wang K, Zhang C H, Wang G W, Li F S and Wang T 2023 Phys. Scr. 98 045917
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